Abstract
We give an explicit formula for the Higgs and Coulomb branch Hilbert series for the class of 3d \( \mathcal{N}=4 \) superconformal gauge theories T σ ρ (G) corresponding to a set of D3 branes ending on NS5 and D5-branes, with or without O3 planes. Here G is a classical group, σ is a partition of G and ρ a partition of the dual group G ∨. In deriving such a formula we make use of the recently discovered formula for the Hilbert series of the quantum Coulomb branch of \( \mathcal{N}=4 \) superconformal theories. The result can be expressed in terms of a generalization of a class of symmetric functions, the Hall-Littlewood polynomials, and can be interpreted in mathematical language in terms of localization. We mainly consider the case G = SU(N) but some interesting results are also given for orthogonal and symplectic groups.
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Cremonesi, S., Hanany, A., Mekareeya, N. et al. T σ ρ (G) theories and their Hilbert series. J. High Energ. Phys. 2015, 150 (2015). https://doi.org/10.1007/JHEP01(2015)150
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DOI: https://doi.org/10.1007/JHEP01(2015)150